The measure 0 of an angle in standard position is given. Find the exact values of cos 0 and sin 0 for the angle measure. Show your work.
7π/4 radians
To find the exact values of cos(7π/4) and sin(7π/4), we need to determine the coordinates of the point on the unit circle that corresponds to that angle.
First, let's draw the unit circle. The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane.
Next, we need to determine the coordinates on the unit circle that correspond to the angle 7π/4 radians. To do this, we can use the properties of the unit circle and the trigonometric functions.
The angle 7π/4 radians is located in the fourth quadrant of the unit circle. In this quadrant, the x-coordinate is negative and the y-coordinate is negative.
In the first quadrant, where the angle is π/4 radians, the x-coordinate is cos(π/4) = 1/sqrt(2) and the y-coordinate is sin(π/4) = 1/sqrt(2).
Since the angle 7π/4 radians is in the fourth quadrant, the coordinates will have opposite signs. Therefore, the x-coordinate is -1/sqrt(2) and the y-coordinate is -1/sqrt(2).
So, cos(7π/4) = -1/sqrt(2) and sin(7π/4) = -1/sqrt(2).